Research methodology

Beyond the Square-Root Barrier: Automated Discovery of Algebraic and Algorithmic Shortcuts in Bitcoin Cryptography

A hypothesis-driven, reproducible study of secp256k1, ECDSA, BIP340 Schnorr and SHA-256 with machine-checked identities and controlled negative results

Simon-Pierre Boucher · UQO Working Papers · November 2026 · v1.0

Bitcoin's security rests on the elliptic-curve discrete-logarithm problem on secp256k1, on SHA-256, and on the ECDSA and BIP340 Schnorr signature schemes. The generic cost of the discrete logarithm, Θ(√n), is a theorem in the generic-group model; the curve's unusual structure, a special prime, j-invariant 0 and…

Zero-Forcing Bounds for Generalized Petersen Graphs: Computational Discovery and Certified Proofs for P(n,5)

Simon-Pierre Boucher · UQO Working Papers · October 2026 · v1.0

The zero forcing number Z(G) of a graph is the minimum size of a set of initially black vertices from which the colour-change rule (a black vertex with exactly one white neighbour forces that neighbour black) eventually colours the whole graph; it bounds the maximum nullity of the matrices described by G. For the…

Protocol-Guided Autonomous Research with Claude Code

Scientific Verification, Reproducibility, and the Cost of Delegation: A Controlled Study

Simon-Pierre Boucher · UQO Working Papers · October 2026 · v1.0

Instruction files that steer coding agents through research tasks range from one sentence to several thousand words of phases, gates and integrity rules, but whether that structure changes what the agent delivers has not been measured with the agent held fixed. The paper reports 288 live Claude Code runs (362…

VQuant: An Agentic Large Language Model Architecture for Automated Quantitative Financial Analysis and Document Generation

Reasoning-Augmented Tool Orchestration, In-Loop Numerical Computation, and Multi-Format Reporting

Simon-Pierre Boucher · UQO Working Papers · October 2026 · v1.1

Large language models write fluently about finance, but fluency does not make a number correct, current, or reproducible. This paper is a design-science description of VQuant, a deployed web platform that couples a reasoning-capable LLM with a deterministic execution substrate so that a natural-language request…